Game theory

Any number of people, from John Maynard Keynes and Jesse Livermore downwards, have viewed the way the stockmarket operates as being like a 'game'. Among more recent contributors to this idea have been those who draw analogies with the stockmarket as a poker game. Others try and apply 'game theory' to the stockmarket.

You cannot go far along the path of researching game theory without encountering John von Neumann.

Von Neumann was a Hungarian-born Princeton mathematics professor and a member of the team working on the Manhattan Project, America's race to produce an atomic bomb. He was also closely involved in devising the theory and architecture that allowed the invention of the personal computer, as well as in devising theories subsequently used in computer programming.

He is however remembered principally for the development, with fellow Princeton economist Oskar Morgernstern, of game theory. Game theory is a means of using mathematical concepts to analyse decision-making in a competitive situation involving a conflict of one sort or another. Their theory was articulated in the book The Theory of Games and Economic Behaviour, published in 1944.

It is impossible to understate how influential this theory has been in politics and world affairs, economics, business and the stockmarket. Von Neumann is credited with devising the Cold War concept of Mutually Assured Destruction. And there are few areas of business decision-making that cannot benefit from knowledge of game theory.

One of the most complex games

In game theory terms, the stockmarket is a zero-sum, multi-player game against nature, one of the most complex games to model. You, as an investor, are playing a game against the market. Making a profit doesn't rely on your actions alone, but on the behaviour of all the other players, as expressed by the market's own fluctuations.

Decisions in the market are taken under a combination of risk and uncertainty and in a condition where not all players in the market have the benefit of the same level of information or the power to interpret it correctly.

The other intriguing fact of the stockmarket as a game is that, in totality, the stockmarket is a zero-sum game. The sum of all the gains must equate to the sum of all the losses, even though individual transactions need not conform to this rule.

The flaw in the idea of using game theory to make stockmarket decisions is that to use game theory modelling accurately requires precise assumptions, which may be overturned at any time by an external event.

One can, for example, make an assumption that on the basis of a given level of market volatility, strategy x may be preferred over strategy y, but then the whole basis of the game may be overturned by an external event like an earthquake or terrorist attack.

That said, many problems of investment strategy can be solved through the use of the pattern of reasoning developed in game theory, such as the balancing of risk and profit, and the use of stop-losses.

Peter says

Game theory, though abstruse, is far from being irrelevant to stockmarket investors. The structure of the auction of 3G wireless spectrum was, it is rumoured, devised with an eye to the principles of game theory. Game theorists won the 1994 Nobel Prize for Economics.

The real benefit of game theory for investors is that it teaches caution and an appreciation of the very real risk of an external, or even market-generated, event derailing a carefully thought-out strategy.

This should be so obvious as not to require any further teaching, but even experienced investors caught out by the evolution of the credit crunch and the market's reaction to it will attest to the need to appreciate lessons such as this. The terrorist attacks of 9/11, and the Kobe earthquake and the Russian bond default in late 1990s are other examples.

The books on the subject that do exist (Gaming the Market, by Ronald Shelton, published by John Wiley, is a good example) focus on applying the techniques of game theory to techniques that can be used by short term traders. For those of that turn of mind they are a worthwhile read.

But longer term fundament investors also need to keep a weather eye on game theory too, if only to remind themselves that the market, and other players in the game, can often spring a surprise.

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